Question
Find the value of z in parallelogram RSTU.
T
U
R
S
z+60°
z
z=
°
T
U
R
S
z+60°
z
z=
°
Answers
GPT-4o mini
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their sum is \(180^\circ\)).
Given the angles:
- Let's assume \(\angle R = z + 60^\circ\)
- \(\angle S = z\)
Since R and S are consecutive angles, we can write the equation:
\[
(z + 60^\circ) + z = 180^\circ
\]
Now, combine like terms:
\[
2z + 60^\circ = 180^\circ
\]
Next, subtract \(60^\circ\) from both sides:
\[
2z = 120^\circ
\]
Now, divide by 2:
\[
z = 60^\circ
\]
So the value of \(z\) in the parallelogram RSTU is \(60^\circ\).
Given the angles:
- Let's assume \(\angle R = z + 60^\circ\)
- \(\angle S = z\)
Since R and S are consecutive angles, we can write the equation:
\[
(z + 60^\circ) + z = 180^\circ
\]
Now, combine like terms:
\[
2z + 60^\circ = 180^\circ
\]
Next, subtract \(60^\circ\) from both sides:
\[
2z = 120^\circ
\]
Now, divide by 2:
\[
z = 60^\circ
\]
So the value of \(z\) in the parallelogram RSTU is \(60^\circ\).